The continued fractions found in the unorganized portions of Ramanujan’s notebooks
About this Title
G. E. Andrews, Bruce C. Berndt, Lisa Jacobsen and Robert L. Lamphere
Publication: Memoirs of the American Mathematical Society
Publication Year 1992: Volume 99, Number 477
ISBNs: 978-0-8218-2538-9 (print); 978-1-4704-0903-6 (online)
MathSciNet review: 1124109
MSC: Primary 11A55; Secondary 01A60, 05A19, 11B65
Among his thirty-three published papers, Ramanujan had only one continued fraction, the Rogers-Ramanujan continued fraction. However, his notebooks contain over 100 results on continued fractions. At the end of his second notebook are 100 pages of unorganized material, and the third notebook comprises thirty-three pages of disorganized results. In these 133 pages of material are approximately sixty theorems on continued fractions, most of them new results. In this monograph, the authors discuss and prove each of these theorems. Aimed at those interested in Ramanujan and his work, this monograph will be of special interest to those who work in continued fractions, $q$-series, special functions, theta-functions, and combinatorics. The work is likely to be of interest to those in number theory as well. The only required background is some knowledge of continued fractions and a course in complex analysis.
Researchers in continued fractions, $q$-series, special functions, theta-functions, combinatorics, and those interested in number theory as well.
Table of Contents
- Proofs of entries 1–60